The inverse source problems, as an important research subject in inverse scattering theory, have significant applications in diverse scientific and industrial areas such as antenna design and synthesis, medical imaging, optical tomography, and fluorescence microscopy. Although they have been extensively studied by many researchers, some of the fundamental questions, such as uniqueness, stability, and uncertainty quantification, still remain to be answered.
In this talk, our recent progress will be discussed on the inverse source problems for acoustic, elastic, and electromagnetic waves. I will present a new approach to solve the stochastic inverse source problem, which is to determine the statistical properties of the random source. The stability will be addressed for the deterministic counterparts of the inverse source problems. We show that the increasing stability can be achieved by using the Dirichlet boundary data at multiple frequencies. Some ongoing projects will be highlighted in random medium and time-domain inverse problems.